A simple relaying strategy for diamond networks

We consider a Gaussian diamond network where a source communicates with the destination through n non-interfering half-duplex relays. Using simple approximations to the capacity of the network, we show that simple relaying strategies involving two relays and two scheduling states can achieve at least half the capacity of the whole network, independent of channel SNRs. The proof uses linear programming duality and implies an algorithm to find such a pair of relays in O(n log n) time(1).